Grab vs. composite sampling of particulate materials with significant spatial heterogeneity—A simulation study of “correct sampling errors”

Sampling errors can be divided into two classes, incorrect sampling and correct sampling errors. Incorrect sampling errors arise from incorrectly designed sampling equipment or procedures. Correct sampling errors are due to the heterogeneity of the material in sampling targets. Excluding the incorrect sampling errors, which can all be eliminated in practice although informed and diligent work is often needed, five factors dominate sampling variance: two factors related to material heterogeneity (analyte concentration; distributional heterogeneity) and three factors related to the sampling process itself (sample type, sample size, sampling modus). Due to highly significant interactions, a comprehensive appreciation of their combined effects is far from trivial and has in fact never been illustrated in detail. Heterogeneous materials can be well characterized by the two first factors, while all essential sampling process characteristics can be summarized by combinations of the latter three. We here present simulations based on an experimental design that varies all five factors. Within the framework of the Theory of Sampling, the empirical Total Sampling Error is a function of the fundamental sampling error and the grouping and segregation error interacting with a specific sampling process. We here illustrate absolute and relative sampling variance levels resulting from a wide array of simulated repeated samplings and express the effects by pertinent lot mean estimates and associated Root Mean Squared Errors/sampling variances, covering specific combinations of materials’ heterogeneity and typical sampling procedures as used in current science, technology and industry. Factors, levels and interactions are varied within limits selected to match realistic materials and sampling situations that mimic, e.g., sampling for genetically modified organisms; sampling of geological drill cores; sampling during off-loading 3-dimensional lots (shiploads, railroad cars, truckloads etc.) and scenarios representing a range of industrial manufacturing and production processes. A new simulation facility “SIMSAMP” is presented with selected results designed to show also the wider applicability potential. This contribution furthers a general exposé of all essential effects in the regimen covered by “correct sampling errors”, valid for all types of materials in which non-bias sampling can be achieved.     

Development and validation of a new direct sampling method for coarse mono- and mixed waste fractions bound in bales

Sampling of coarse waste materials is considered to be a particularly challenging task and is at the same time the most crucial step in the overall data acquisition process. Despite this fact, research work on new sampling methods or new scientific approaches to sampling has been rather limited over the last decades. This paper focuses on a completely new sampling procedure for coarse two-dimensional materials similar to municipal solid waste or packaging plastics. The developed method is especially suitable for materials with particle sizes >100 mm and is based on the ‘press-and-drill method’ introduced by researchers from Fachhochschule Nordhausen. The basic idea is to sample the material in its compressed form (e.g. as bales) with a drilling tool in order to gain increments. The study presented in this paper shows the results of two extensive test series applying this new sampling technique to a middle-calorific fraction produced from packaging material (mainly plastics, textiles and paper). In parallel, the state-of-the-art approach was also applied on the same materials to gain valuable reference data. Results from both approaches are used for the extensive validation of the new sampling method. The verification of accuracy was realised by doping the material with defined pieces of foil containing molybdenum sulphide (MoS₂) which acted as a tracer in the bale. The results obtained by the new direct bale sampling showed not only good accordance with the actual tracer content in each bale but also with results derived from the state-of-the-art approach. In this study, homogeneously distributed parameters (e.g. loss of ignition) were included just as inhomogeneously distributed elements (i.e. Cu). It is shown that sufficient representativeness for coarse materials (d₉₅ > 300 mm) is obtained despite relatively small sample amounts and without previous comminution of the material.     

X射线荧光光谱法在电气石标准物质均匀性检验中的应用

采用粉末压片–X射线荧光光谱法对电气石标准物质候选物的均匀性进行检验。选择Si,Al,Mg,Fe,Ca,Na等6个元素作为检验元素,样品以随机方式进行测量,根据单因素方差分析的F值和测定值的相对标准偏差(RSD)判定样品的均匀性,并计算了检测方法的误差和样品不均匀误差。结果表明,方差检验的F计算值在0.80~1.93之间,小于F临界值1.96,测定结果的相对标准偏差小于0.9%;检测方法相对标准偏差和样品不均匀度(以RSD表示)均小于0.5%,说明制备的电气石标准物质候选物具有良好的均匀性。通过公式计算,确定最小取样量为200 mg。该方法无需湿法分解样品,绿色环保,简便快速,测定结果精密度高。     

Determining the variability associated with testing shelled corn for aflatoxin using different analytical procedures in Louisiana in 1998

The number of elevator facilities with laboratories to test shelled corn for aflatoxin on site is increasing. The inherent difficulty in accurately determining the true aflatoxin concentration of a lot of corn may have serious implications. Deviations from the true value are of even greater significance at busy locations where a high throughput is desired. This study was instituted to measure (1) the differences in aflatoxin test results between elevator laboratories and the Louisiana Agricultural Chemistry (LAC) laboratory and (2) the variability in aflatoxin test results associated with sampling, sample preparation, and analysis of shelled corn at such locations. One hundred lots of shelled corn from 10 elevators in Louisiana were analyzed for aflatoxin using the Aflatest method (at elevators and at the LAC laboratory) and high-performance column liquid chromatography (HPLC; LAC laboratory only). Mean aflatoxin levels determined at elevator laboratories were significantly (P < 0.05) lower from those obtained in the LAC laboratory using the Aflatest method. Overall, Aflatest method results were lower than those obtained by HPLC. This difference may be attributed to analyst technical dexterity, difficulty in providing careful attention to detail in a high throughput environment, and/or substandard facilities found at elevators. The total variance was partitioned into the combined sampling plus subsampling variance and analytical variance. The sampling and sample preparation steps accounted for about 91.5% of the total variability. When using the HPLC analytical method, the analytical step contributed only 8.5% to the total variance.     

Effect of missing values in estimation of mean of auto-correlated measurement series

Sampling and uncertainty of sampling are important tasks, when industrial processes are monitored. Missing values and unequal sources can cause problems in almost all industrial fields. One major problem is that during weekends samples may not be collected. On the other hand a composite sample may be collected during weekend. These systematically occurring missing values (gaps) will have an effect on the uncertainties of the measurements. Another type of missing values is random missing values. These random gaps are caused, for example, by instrument failures. Pierre Gy's sampling theory includes tools to evaluate all error components that are involved in sampling of heterogeneous materials. Variograms, introduced by Gy's sampling theory, have been developed to estimate the uncertainty of auto-correlated process measurements. Variographic experiments are utilized for estimating the variance for different sample selection strategies. The different sample selection strategies are random sampling, stratified random sampling and systematic sampling. In this paper both systematic and random gaps were estimated by using simulations and real process data. These process data were taken from bark boilers of pulp and paper mills (combustion processes). When systematic gaps were examined a linear interpolation was utilized. Also cases introducing composite sampling were studied. Aims of this paper are: (1) how reliable the variogram is to estimate the process variogram calculated from data with systematic gaps, (2) how the uncertainty of missing gap can be estimated in reporting time-averages of auto-correlated time series measurements. The results show that when systematic gaps were filled by linear interpolation only minor changes in the values of variogram were observed. The differences between the variograms were constantly smallest with composite samples. While estimating the effect of random gaps, the results show that for the non-periodic processes the stratified random sampling strategy gives more reliable results than systematic sampling strategy. Therefore stratified random sampling should be used while estimating the uncertainty of random gaps in reporting time-averages of auto-correlated time series measurements.     

Testing shelled corn for aflatoxin, Part I: estimation of variance components

The variability associated with testing lots of shelled corn for aflatoxin was investigated. Eighteen lots of shelled corn were tested for aflatoxin contamination. The total variance associated with testing shelled corn was estimated and partitioned into sampling, sample preparation, and analytical variances. All variances increased as aflatoxin concentration increased. With the use of regression analysis, mathematical expressions were developed to model the relationship between aflatoxin concentration and the total, sampling, sample preparation, and analytical variances. The expressions for these relationships were used to estimate the variance for any sample size, subsample size, and number of analyses for a specific aflatoxin concentration. Test results on a lot with 20 parts per billion aflatoxin using a 1.13 kg sample, a Romer mill, 50 g subsamples, and liquid chromatographic analysis showed that the total, sampling, sample preparation, and analytical variances were 274.9 (CV = 82.9%), 214.0 (CV = 73.1 %), 56.3 (CV = 37.5%), and 4.6 (CV = 10.7%), respectively. The percentage of the total variance for sampling, sample preparation, and analytical was 77.8, 20.5, and 1.7, respectively.     

Analysis of solid samples by ICP-mass spectrometry

Summary ICP-Mass spectrometry is typically used as a technique for very rapid multielement analysis at trace and ultra-trace levels of solutions by continuous sample aspiration and nebulization. However, ICP-MS is well suited to be used as a detector for other sample introduction devices. For the analysis of solid samples laser sampling and electrothermal vaporization accessories may be used as sample introduction devices for ICP-MS. Laser sampling permits the analysis of many different types of solid materials. For solid sampling ETV-ICP-MS analysis it is of advantage to reduce the sample to a fine powder prior to analysis. For automated analysis powders may be introduced as slurries into the graphite furnace by means of a slurry sampling device. Since appropriate certified solid reference materials are not always available for calibration, or since they are not certified for all analyte elements of interest, the analyses discussed in this contribution were performed semiquantitatively. The instrument response function was established using reference materials which were similar in their composition to the samples. The results of semiquantitative bulk analyses of glass (NIST 612) and geological material (USGS GXR-3) by laser sampling ICP-MS are in good agreement with the certified values. The concentrations of the analytes determined in the glass sample were in the range of 10 g/g to 80 g/g. The lowest analyte concentration in the geological sample was 0.4 g/g (Eu) and the highest was approximately 186 mg/g (Fe). The precision achieved was in the order of 5% to 15%. Laser sampling ICP-MS is not only suitable to bulk analysis but also to analyses where spatial information is required. As an example for such an application the determination of Pb in a wine bottle cork stopper is dicussed. The slurry sampling technique was used for the semiquantitative analysis of NIST coal reference samples by electrothermal vaporization ICP-MS. The accuracy achieved with this approach was within a factor of ±2 of the reference values.     

Sampling almonds for aflatoxin, part I: estimation of uncertainty associated with sampling, sample preparation, and analysis

Domestic and international regulatory limits have been established for aflatoxin in almonds and other tree nuts. It is difficult to obtain an accurate and precise estimate of the true aflatoxin concentration in a bulk lot because of the uncertainty associated with the sampling, sample preparation, and analytical steps of the aflatoxin test procedure. To evaluate the performance of aflatoxin sampling plans, the uncertainty associated with sampling lots of shelled almonds for aflatoxin was investigated. Twenty lots of shelled almonds were sampled for aflatoxin contamination. The total variance associated with measuring B1 and total aflatoxins in bulk almond lots was estimated and partitioned into sampling, sample preparation, and analytical variance components. All variances were found to increase with an increase in aflatoxin concentration (both B1 and total). By using regression analysis, mathematical expressions were developed to predict the relationship between each variance component (total, sampling, sample preparation, and analysis variances) and aflatoxin concentration. Variance estimates were the same for B1 and total aflatoxins. The mathematical relationships can be used to estimate each variance for a given sample size, subsample size, and number of analyses other than that measured in the study. When a lot with total aflatoxins at 15 ng/g was tested by using a 10 kg sample, a vertical cutter mixer type of mill, a 100 g subsample, and high-performance liquid chromatography analysis, the sampling, sample preparation, analytical, and total variances (coefficient of variation, CV) were 394.7 (CV, 132.4%), 14.7 (CV, 25.5%), 0.8 (CV, 6.1%), and 410.2 (CV, 135.0%), respectively. The percentages of the total variance associated with sampling, sample preparation, and analytical steps were 96.2, 3.6, and 0.2, respectively.     

Sampling hazelnuts for aflatoxin: uncertainty associated with sampling, sample preparation, and analysis

The variability associated with the aflatoxin test procedure used to estimate aflatoxin levels in bulk shipments of hazelnuts was investigated. Sixteen 10 kg samples of shelled hazelnuts were taken from each of 20 lots that were suspected of aflatoxin contamination. The total variance associated with testing shelled hazelnuts was estimated and partitioned into sampling, sample preparation, and analytical variance components. Each variance component increased as aflatoxin concentration (either B1 or total) increased. With the use of regression analysis, mathematical expressions were developed to model the relationship between aflatoxin concentration and the total, sampling, sample preparation, and analytical variances. The expressions for these relationships were used to estimate the variance for any sample size, subsample size, and number of analyses for a specific aflatoxin concentration. The sampling, sample preparation, and analytical variances associated with estimating aflatoxin in a hazelnut lot at a total aflatoxin level of 10 ng/g and using a 10 kg sample, a 50 g subsample, dry comminution with a Robot Coupe mill, and a high-performance liquid chromatographic analytical method are 174.40, 0.74, and 0.27, respectively. The sampling, sample preparation, and analytical steps of the aflatoxin test procedure accounted for 99.4, 0.4, and 0.2% of the total variability, respectively.     

Approaches to Sampling and Sample Pretreatments for Metal Speciation in Soils and Sediments

Abstract

The main aspects of sampling and sample pretreatment in metal speciation studies of soils and sediments are discussed. The risks of sample contamination by the use of inappropriate materials, containers and tools as well as the possibilities of losses of analyte during sample handling are pointed out. Field sampling methods are described and minimum sample weight criteria for representative sampling of dry soils are presented. Sampling by traps and continuous flow centrifugation methods for suspended sediments and of bottom sediments by grabs or corers are compared. To avoid significant changes in some metal species drying and storage temperatures may need to be controlled and preservation in an inert atmosphere or by irradiation is discussed. The difficulties of establishing definitive protocols for sampling and sample pretreatment are emphasized as well as the need for selecting the appropriate technique in each particular case.     

Sampling, sample preparation, and analytical variability associated with testing wheat for deoxynivalenol

The variability associated with testing wheat for deoxynivalenol (DON) was measured using a 0.454 kg sample, Romer mill, 25 g comminuted subsample, and the Romer Fluoroquant analytical method. The total variability was partitioned into sampling, sample preparation, and analytical variability components. Each variance component was a function of the DON concentration and equations were developed to predict each variance component using regression techniques. The effect of sample size, subsample size, and number of aliquots on reducing the variability of the DON test procedure was also determined. For the test procedure, the coefficient of variation (CV) associated with testing wheat at 5 ppm was 13.4%. The CVs associated with sampling, sample preparation, and analysis were 6.3, 10.0, and 6.3%, respectively. For the sample variation, a 0.454 kg sample was used; for the sample preparation variation, a Romer mill and a 25 g subsample were used; for the analytical variation, the Romer Fluoroquant method was used. The CVs associated with testing wheat are relatively small compared to the CV associated with testing other commodities for other mycotoxins, such as aflatoxin in peanuts. Even when the small sample size of 0.454 kg was used, the sampling variation was not the largest source of error as found in other mycotoxin test procedures.     

固体分层取样方案的最优化设计

本文首次从理论上探讨了取得量对分层取样误差的影响,提出了总取样量一定时各层的最佳取样量和最小取样方差的计算公式,从而为分层取样的最佳取样方案设计提供了理论依据。     

Sampling and analytical variability associated with the determination of aflatoxins and ochratoxin A in bulk lots of powdered ginger marketed in 1-lb bags

Ginger has been used as a food, dietary supplement, and condiment for centuries. Mycotoxins such as the aflatoxins (AF) and ochratoxin A (OTA) have been reported in ginger roots in several studies. It is important to design effective sampling methods that will accurately and precisely predict the true mycotoxin level in a bulk lot. The objective of this study was to measure the sampling and analytical variability associated with the test procedure used to measure AF and OTA in a bulk lot of powdered ginger using a 5-g laboratory sample and HPLC analytical methods. Twelve 5-g laboratory samples were taken from each of two lots. Duplicate aliquots were removed from each 5-g laboratory sample/solvent blend, and each aliquot was simultaneously analyzed for AF and OTA by HPLC analytical methods. Using a balanced nested design, the total variance associated with the above AF and OTA test procedures was partitioned into sampling and analytical variance components for each lot. Averaged across both lots, the sampling and analytical variances accounted for 87% and 13% of the total variance, respectively, for AF and 97% and 3%, respectively, for OTA. The sampling and analytical coefficients of variation were 9.5% and 3.6%, respectively, for AF, and 16.6% and 2.9%, respectively, for OTA when using a single 5-g laboratory sample and HPLC analytical methods. Equations are derived to show the effect of increasing laboratory sample size and/or number of aliquots on reducing the variability of the test procedures used to estimate OTA and AF in powdered ginger.     

Sampling almonds for aflatoxin, part II: estimating risks associated with various sampling plan designs

About 100 nations have established regulatory limits for aflatoxin in food and feeds. Because these limits vary widely from one country to another, the Codex Alimentarius Commission, working through the Codex Committee on Food Additives and Contaminants, has initiated work to harmonize aflatoxin limits and sampling plans for almonds, pistachios, hazelnuts, and Brazil nuts. Studies were developed to measure the uncertainty and distribution among test results for replicate samples taken from aflatoxin-contaminated almond shipments. The uncertainty and distribution information was used to develop a model to evaluate the performance of aflatoxin sampling plans so that harmonized sampling plans can be developed for almonds that reduce the misclassifying of lots in the export trade. Twenty lots of shelled almonds were sampled according to an experimental protocol in which sixteen 10 kg samples were taken from each lot. The observed aflatoxin distribution among the 16 sample test results was compared with 3 theoretical distributions. The negative binomial distribution was selected to model aflatoxin distribution among sample test results because it gave acceptable fits across all 20 observed sample distributions. By using the variance and distribution information, operating characteristics curves were developed to predict the effect of sample size and accept/reject limits on the probability of rejecting good lots and accepting bad lots.     

Determination of Lead in Lipstick by Direct Solid Sampling High-Resolution Continuum Source Graphite Furnace Atomic Absorption Spectrometry: Comparison of Two Digestion Methods

A new analytical procedure for the determination of lead in lipstick has been developed using direct solid sampling high resolution continuum source graphite furnace atomic absorption spectrometry (SS HR CS GFAAS). The performance of this method has been compared to acid digestion methods for sample preparation, with or without hydrofluoric acid (HF) with inductively coupled plasma mass spectrometry (ICP-MS) detection. Good reliability was obtained for all three methods; the results obtained for certified reference materials with concentrations between 1 and 20 ppm were in agreement with the certified values. However, for materials with complex matrices, such as pearl or Ca-Na borosilicate, only ICP-MS with HF sample digestion or AAS with direct solid sampling allowed complete recovery of lead. To avoid the use of hazardous acids, the development of SS HR CS GFAAS is an interesting alternative. With the AAS method, a characteristic mass of 13.2 pg of lead was obtained, and the limit of detection was 0.005 µg/g. The performance of the method was evaluated by determining lead in lipstick. The use of the solid sampling technique constitutes a good alternative for accurate and rapid determination of lead content in lipstick and cosmetic raw materials, with a suitable limit of detection and a reduced risk of contamination or of analyte loss. Another alternative would be to use ICP-MS determination in conjunction with microwave-assisted acid digestion without the use of HF, which implies accepting a quantification of “nearly total” lead, closer to a “bio-extractible” fraction.     

Distribution among sample test results when testing shelled corn lots for fumonisin.

The statistical distribution known as the compound gamma function was studied for suitability in describing the distribution of sample test results associated with testing lots of shelled corn for fumonisin. Thirty-two 1.1 kg test samples were taken from each of 16 contaminated lots of shelled corn. An observed distribution consisted of 32 sample fumonisin test results for each lot. The mean fumonisin concentration, c, and the variance, s2, among the 32 sample fumonisin test results along with the parameters for the compound gamma function were determined for each of the 16 observed distributions. The 16 observed distributions of sample fumonisin test results were compared with the compound gamma function using the Power Divergence test. The null hypothesis that the observed distribution could have resulted from sampling a family of compound gamma distributions was not rejected at the 5% significance level for 15 of the 16 lots studied. Parameters of the compound gamma distribution were calculated from the 32-fumonisin sample test results using the method of moments. Using regression analysis, equations were developed that related the parameters of the compound gamma distribution to fumonisin concentration and the variance associated with a fumonisin test procedure. An operating characteristic curve was developed for a fumonisin sampling plan to demonstrate the use of the compound gamma function.     

Testing green coffee for ochratoxin A, part I: estimation of variance components

The variability associated with testing lots of green coffee beans for ochratoxin A (OTA) was investigated. Twenty-five lots of green coffee were tested for OTA contamination. The total variance associated with testing green coffee was estimated and partitioned into sampling, sample preparation, and analytical variances. All variances increased with an increase in OTA concentration. Using regression analysis, mathematical expressions were developed to model the relationship between OTA concentration and the total, sampling, sample preparation, and analytical variances. The expressions for these relationships were used to estimate the variance for any sample size, subsample size, and number of analyses for a specific OTA concentration. Testing a lot with 5 microg/kg OTA using a 1 kg sample, Romer RAS mill, 25 g subsamples, and liquid chromatography analysis, the total, sampling, sample preparation, and analytical variances were 10.75 (coefficient of variation [CV] = 65.6%), 7.80 (CV = 55.8%), 2.84 (CV = 33.7%), and 0.11 (CV = 6.6%), respectively. The total variance for sampling, sample preparation, and analytical were 73, 26, and 1%, respectively.     

Calibration of solid sampling Zeeman atomic absorption spectrophotometry by extrapolation to zero matrix

Summary A new method is described for the calibration of solid sampling Zeeman atomic absorption spectrophotometry, which can be applied independently of the use of certified reference materials. The specific signal (peak height divided by analyte mass or peak height divided by sample mass, for standard and sample, resp.) is plotted as a function of the analyte or the sample mass, and the line is extrapolated to zero mass. It is believed that this gives a specific signal not influenced by deviations from linearity of the calibration curve and free from matrix effects. The method yielded good results for Zn, Cd and Pb in several certified reference materials.Presented at the 5th International Colloquium on Solid Sampling with Atomic Spectroscopy, May 18–20, 1992; Geel, Belgium. Papers edited by R. F. M. Herber, Amsterdam